Optimization Under Uncertainty of Nonlinear Energy Sinks

Nonlinear Energy Sinks (NES) are used to passively reduce the amplitude of vibrations. This reduction is made possible by introducing a nonlinearly stiffening behavior in the NES, which might lead to an irreversible transfer of energy between the main system (e.g., a building) and the NES. However, this irreversible transfer, and therefore the efficiency of the NES, is strongly dependent on the design parameters of the NES. In fact, the efficiency of the NES might be so sensitive to changes in design parameters and other factors (e.g., initial conditions) that it is discontinuous, switching from efficiency to inefficiency for a small perturbation of parameters. For this reason, this work introduces a novel technique for the optimization under uncertainty of NES. The approach is based on a support vector machine classifier, which is insensitive to discontinuities and allows one to efficiently propagate uncertainties. This enables one to efficiently solve an optimization under uncertainty problem. The various techniques presented in this paper are applied to an analytical NES example.Copyright © 2014 by ASME

[1]  Oleg Gendelman,et al.  Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture , 2001 .

[2]  Claude-Henri Lamarque,et al.  Nonlinear Energy Sink With Uncertain Parameters , 2006 .

[3]  Alexander F. Vakakis,et al.  Experimental Testing and Numerical Simulation of a Six-Story Structure Incorporating Two-Degree-of-Freedom Nonlinear Energy Sink , 2014 .

[4]  D. M. McFarland,et al.  Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame: Computational results , 2008 .

[5]  Alexander F. Vakakis,et al.  Dynamics of a linear beam with an attached local nonlinear energy sink , 2007 .

[6]  Gaëtan Kerschen,et al.  Nonlinear vibration absorber coupled to a nonlinear primary system: A tuning methodology , 2009 .

[7]  L. Scaff.  Lawrence A , 2005 .

[8]  Samy Missoum,et al.  Reliability-Based Design Optimization of Nonlinear Aeroelasticity Problems , 2010 .

[9]  G. B. Warburton,et al.  Optimum absorber parameters for various combinations of response and excitation parameters , 1982 .

[10]  B. F. Spencer,et al.  Numerical Study of Nonlinear Energy Sinks for Seismic Response Reduction , 2011 .

[11]  Claude-Henri Lamarque,et al.  Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results , 2007 .

[12]  Alexander F. Vakakis,et al.  Targeted Energy Transfer Between a Model Flexible Wing and Nonlinear Energy Sink , 2010 .

[13]  Oleg Gendelman,et al.  Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber , 2007 .

[14]  A. P,et al.  Mechanical Vibrations , 1948, Nature.

[15]  Oleg Gendelman,et al.  Energy pumping in nonlinear mechanical oscillators : Part I : Dynamics of the underlying Hamiltonian systems , 2001 .

[16]  Nello Cristianini,et al.  Support Vector Machines and Kernel Methods: The New Generation of Learning Machines , 2002, AI Mag..

[17]  R. Brereton,et al.  Support vector machines for classification and regression. , 2010, The Analyst.

[18]  Stephane Hess,et al.  On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice , 2006 .

[19]  A. I. Musienko,et al.  Dynamic interaction of a semi-infinite linear chain of coupled oscillators with a strongly nonlinear end attachment , 2003 .

[20]  Alexander F. Vakakis,et al.  Use of non‐linear localization for isolating structures from earthquake‐induced motions , 1999 .

[21]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[22]  Vicente J. Romero,et al.  Comparison of pure and "Latinized" centroidal Voronoi tessellation against various other statistical sampling methods , 2006, Reliab. Eng. Syst. Saf..

[23]  Pierre-Olivier Mattei,et al.  Toward an adjustable nonlinear low frequency acoustic absorber , 2011 .

[24]  Samy Missoum,et al.  Reliability-based Design Optimization of Nonlinear Energy Sinks , 2015 .

[25]  Pierre-Olivier Mattei,et al.  Enhancing the dynamic range of targeted energy transfer in acoustics using several nonlinear membrane absorbers , 2012, 1407.4904.

[26]  Alexander F. Vakakis,et al.  Enhancing the Robustness of Aeroelastic Instability Suppression Using Multi-Degree-of-Freedom Nonlinear Energy Sinks , 2008 .

[27]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[28]  Stephane Pernot,et al.  Design criteria for optimally tuned nonlinear energy sinks—part 1: transient regime , 2012 .

[29]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[30]  Samy Missoum,et al.  A Sampling-Based Approach for Probabilistic Design with Random Fields , 2008 .

[31]  Samy Missoum,et al.  Reliability-based design optimization using Kriging and support vector machines , 2013 .

[32]  Alexander F. Vakakis,et al.  Steady State Passive Nonlinear Energy Pumping in Coupled Oscillators: Theoretical and Experimental Results , 2003 .

[33]  Claude-Henri Lamarque,et al.  Targeted energy transfer with parallel nonlinear energy sinks. Part I: Design theory and numerical results , 2011 .

[34]  G. Kerschen,et al.  Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems , 2008 .

[35]  Bruno Cochelin,et al.  Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber , 2010 .

[36]  Samy Missoum,et al.  A Generalized “Max-Min” Sample for Reliability Assessment With Dependent Variables , 2014 .

[37]  J. A. Hartigan,et al.  A k-means clustering algorithm , 1979 .

[38]  A. Basudhar,et al.  An improved adaptive sampling scheme for the construction of explicit boundaries , 2010 .

[39]  Oleg Gendelman,et al.  Dynamics of a strongly nonlinear vibration absorber coupled to a harmonically excited two-degree-of-freedom system , 2008 .

[40]  Claude-Henri Lamarque,et al.  Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment , 2007 .

[41]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[42]  Carlos Cabrera,et al.  Analysis of the sources of uncertainty for portfolio‐level earthquake loss estimation , 2012 .